Institut des Hautes Etudes Scientifiques (IHES) Courses

Beauty of Life Seen Through Keyhole of Mathematics - Part 1

Explore the intersection of mathematics and biology, from molecular structures to ecological impact, in this thought-provoking lecture on life's fundamental nature.

• YouTube
• 1 hour 44 minutes
• Self-Paced
• Free Video

An Introduction to Super Critical Singularities - Lecture 4: Stability of Implosion

Explore advanced concepts in non-linear PDE singularities, focusing on defocusing problems and their connection to fluid mechanics. Gain insights into key results, open problems, and proof techniques.

• YouTube
• 2 hours 13 minutes
• Self-Paced
• Free Video

An Introduction to Super Critical Singularities - Lecture 3: On Self Similar Solutions for Compressible Euler

Explore self-similar solutions for compressible Euler equations and their role in singularity formation for non-linear PDEs, with connections to fluid mechanics.

• YouTube
• 2 hours 7 minutes
• Self-Paced
• Free Video

An Introduction to Super Critical Singularities - Lecture 2: Front Singularities

Explore front singularities in non-linear PDEs, focusing on defocusing problems and their connection to fluid mechanics. Gain insights into key results, open problems, and proof techniques.

• YouTube
• 2 hours 6 minutes
• Self-Paced
• Free Video

An Introduction to Super Critical Singularities - Lecture 1: Energy Super Critical Singularity Formation

Explore energy super critical singularity formation in non-linear PDEs, focusing on recent discoveries in defocusing problems and their connection to fluid mechanics.

• YouTube
• 1 hour 49 minutes
• Self-Paced
• Free Video

Point-Counting and the Zilber-Pink Conjecture - Lecture 4

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 52 minutes
• Self-Paced
• Free Video

Geometric Laplacians on Self-Conformal Fractal Curves in the Plane

Explore geometric Laplacians on self-conformal fractal curves, examining heat kernels, eigenvalue asymptotics, and their relation to fractal geometry. Delve into construction methods and applications in complex analysis.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Where Do Random Trees Grow Leaves - A Study of Binary Tree Growth Dynamics

Explore the growth patterns of random binary trees, focusing on leaf addition dynamics and fractal properties in tree structures.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Equivalence of Fluctuations Between SHE and KPZ Equation in Weak Disorder Regime

Explore the connection between stochastic heat equation and KPZ equation, demonstrating fluctuation equivalence in weak disorder regime for 3+ dimensions.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Global Solutions to Quadratic Systems of Stochastic Reaction-Diffusion

Explorez les solutions globales des systèmes quadratiques de réaction-diffusion stochastique en dimension deux, avec un accent sur les perturbations à quatre espèces.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Scaling Limits of Disordered Systems

Explore scaling limits of disordered systems, focusing on the Poland-Scheraga model for DNA denaturation and its phase transition effects.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane

Explore particle approximation of the parabolic-parabolic Keller-Segel system in the plane, focusing on stochastic particle systems, tightness, and weak solutions for small sensitivity parameters.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Random Models on Regularity-Integrability Structures

Explore a simplified proof of the BPHZ theorem using extended regularity structures with integrability exponents, advancing the study of singular stochastic partial differential equations.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Regularity Structures for Quasilinear Singular SPDEs

Explore regularity structures for analyzing semilinear and quasilinear parabolic singular stochastic PDEs, suitable for beginners and experts alike.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

An Exact Solution of the Macroscopic Fluctuation Theory

Explore an exact solution of the Macroscopic Fluctuation Theory for diffusive interacting particle systems using Inverse Scattering Theory, focusing on the simple exclusion process.

• YouTube
• 51 minutes
• Self-Paced
• Free Video